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2012 | 10 | 6 | 2264-2271
Tytuł artykułu

On local convexity of nonlinear mappings between Banach spaces

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Języki publikacji
EN
Abstrakty
EN
We find conditions for a smooth nonlinear map f: U → V between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some c and each positive ɛ < c the image f(B ɛ(x)) of each ɛ-ball B ɛ(x) ⊂ U is convex. We give a lower bound on c via the second order Lipschitz constant Lip2(f), the Lipschitz-open constant Lipo(f) of f, and the 2-convexity number conv2(X) of the Banach space X.
Twórcy
autor
  • Ya. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of National Academy of Sciences, 3b Naukova Str., 79060, Lviv, Ukraine, ibanakh@yahoo.com
  • Cracow University of Technology, Warszawska 24, 31-155, Kraków, Poland, plichko@pk.edu.pl
  • AGH University of Science and Technology, Mickiewicza 30, 30-059, Kraków, Poland, pryk.anat@ua.fm
Bibliografia
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  • [2] Borwein J., Guirao A.J., Hájek P., Vanderwerff J., Uniformly convex functions on Banach spaces, Proc. Amer. Math. Soc., 2009, 137(3), 1081–1091 http://dx.doi.org/10.1090/S0002-9939-08-09630-5[Crossref]
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  • [17] Prykarpatska N.K., Blackmore D.L., Prykarpatsky A.K., Pytel-Kudela M., On the inf-type extremality solutions to Hamilton-Jacobi equations, their regularity properties, and some generalizations, Miskolc Math. Notes, 2003, 4(2), 153–180
  • [18] Prykarpatsky A.K., A Borsuk-Ulam type generalization of the Leray-Schauder fixed point theorem, preprint available at http://arxiv.org/abs/0902.4416
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  • [20] Prykarpats’kyi A.K., An infinite-dimensional Borsuk-Ulam-type generalization of the Leray-Schauder fixed-point theorem and some applications, Ukrainian Math. J., 2008, 60(1), 114–120 http://dx.doi.org/10.1007/s11253-008-0046-3[Crossref]
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Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0101-z
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